We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning problem to several commonly used least squaresbased optimization objectives used in system ID. Our comparisons indicate that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods that include differentially constrained least squares and least squares reconstructions of discrete time steppers like dynamic mode decomposition (DMD). These properties allow it to be both more sensitive to new data and less affected by multiple minima -overall yielding a more robust approach. Our theoretical results indicate that least squares and regularized least squares methods like dynamic mode decomposition and sparse identification of nonlinear dynamics (SINDy) can be derived from the probabilistic formulation by assuming noiseless measurements. We also analyze the computational complexity of a Gaussian filter-based approximate marginal Markov Chain Monte Carlo scheme that we use to obtain the Bayesian posterior for both linear and nonlinear problems. We then empirically demonstrate that obtaining the marginal posterior of the parameter dynamics and making predictions by extracting optimal estimators (e.g., mean, median, mode) yields orders of magnitude improvement over the aforementioned approaches. We attribute this performance to the fact that the Bayesian approach captures parameter, model, and measurement uncertainties, whereas the other methods typically neglect at least one type of uncertainty.

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Objective: To report a case of leukopenia associated with paroxetine treatment. Case Summary: A 44-year-old white female with a history of anemia secondary to heavy menses, anxiety, depression, and current tobacco dependence presented with general symptoms of fatigue and blurred vision. The patient's medications at the time of the initial visit were ferrous sulfate 325 mg twice a day and paroxetine 20 mg/day. Three years prior to the initiation of paroxetine, the patient's documented white blood cell (WBC) count was 7.4 × 103/μL with normal differential and hemoglobin was 10.5 g/dL; on presentation, laboratory test results were WBC count 1.3 × 103/μL, red blood cell count 1.78 × 106/μL, hemoglobin 4.5 g/dL, hematocrit 15.1%, and platelets 248 × 103/μL. Three months after discontinuation of paroxetine, the patient's WBC count was 4.4 × 103/μL. Discussion: Paroxetine and other antidepressants have not been known to cause adverse hematologic effects that can be seen with other antipsychotics, namely, clozapine. The use of the Naranjo probability scale indicated a probable relationship between leukopenia and paroxetine therapy in this patient. Based on a MEDLINE search (February 12, 2007), there are limited data on leukopenia as an adverse event of paroxetine. We found this to be a unique case of leukopenia suspected to be secondary to extended use of low-dose paroxetine. Conclusions: Although leukopenia caused by paroxetine and other medications with serotonergic effects appears to be uncommon, physicians and pharmacists should be aware of this rare but potentially serious adverse event.

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This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate predictions far outside the training time interval in the presence of sparse and noisy measurements are possible, which lends robustness and generalizability to the proposed approach. A quantitative benefit is prediction accuracy with less than 10% relative error for more than 12 times longer than a comparable least-squares-based method on a benchmark problem.